Burnett pitched a shutout in his second start since returning from the disabled list, leading the Blue Jays over the Washington Nationals 6-0 Tuesday night.
Burnett (1-1) allowed six hits, struck out seven and didn't walk a batter in just his fourth start of the season.
"My first win as a Blue Jay, it's nice to do it the way I did it," Burnett said.
Expectations were high when Burnett signed a five-year, $55 million contract with Toronto in the offseason, but he missed two months with elbow problems.
He looked solid but got a no-decision against Atlanta on Thursday. He was efficient against Washington, needing only 92 pitches to record his first shutout of the season and the ninth of his career.
"I just pounded the strike zone," said Burnett, who retired 17 of the last 18 batters he faced.
Toronto manager John Gibbons said he needed the victory.
"Now he feels a part of the team," Gibbons said.
Overbay said he was relieved to see Burnett pitch well, considering he's been on the DL twice this season, and he wants to see him make it through a third consecutive start.
"Maybe the third one will show that he's all right to keep going. You always kind of hold your breath on if he's going to get hurt or not," Overbay said.
The Nationals dropped to 1-6 on their nine-game road trip. They've been held to three runs or fewer in all seven games.
It's the second time the former Montreal Expos have played a series in Canada.
"It's tough when you run into a pitcher like we did tonight," Washington's Royce Clayton said. "We drew a tough card."
Manager Frank Robinson said his hitters didn't know what to.
"I don't know what the plan of attack was," Robinson said. "I don't know if we have one. If there was one, we didn't care it out very well."
Toronto's offense has kept the team in contention despite injuries and inconsistent performances from its starting rotation.
Overbay led off the second with a double and scored on Hill's homer to left off Ramon Ortiz (5-6).
Overbay homered to right off Ortiz in the sixth, giving Toronto a 3-0 lead.
The Blue Jays added three runs in the eighth on Hill's RBI double off Jason Bergmann and Alex Rios' two-run single off Bill Bray.
Ortiz allowed three runs and four hits in six innings, his first start in 10 days. The right-hander was scheduled to pitch against Boston last week, but his start was pushed back so he could spend time with his ailing wife.
- Toronto outrighted RHP Josh Towers to Triple-A Syracuse for a second time. Towers, 1-9 with a 9.11 ERA, was first sent to Syracuse on May 24, after opening the season 1-8 in 10 starts. "We're in a spot now where we need to win some more ballgames and hang in this thing and it just wasn't happening for him," Gibbons said.
- Washington 1B Daryle Ward was a late scratch after he couldn't get a flight into Toronto. He had permission to travel separately from the team, but bad weather spoiled his flight plans, a team spokesman said.
- Burnett threw 70 of his 92 pitches for strikes.